Released November 2017 4/5 Small Steps Guidance and Examples Block 4: Length & Perimeter
Year 4/5 Autumn Term Teaching Guidance Overview Small Steps Year 4 Year 5 Kilometres Perimeter on a grid Perimeter of a rectangle Perimeter of rectilinear shapes Converting between units of length Measure perimeter Calculate perimeter Find unknown lengths
Year 4 Autumn Term Teaching Guidance Kilometres Notes and Guidance Here children use their new knowledge of four digit numbers in a real life context. These contexts could include running, swimming, cycling etc. Mathematical Talk If you were to walk for 1km along the road from your school, where would you be? How can you tell if your answer is sensible? Explain to a friend how to convert km to m and vice versa? How far do you travel to school? Do you travel more or less than 1km? Visualise 1km can we measure it out on the school field or the playground? 1 2 3 Varied Fluency Complete the statements. 3000m = km 5km = m 500m = km 9500m = km Complete the bar model. 3 kilometres 1800 metres Use <, > or = to make the statements correct. 500m 7km 5km 11 22 km 800m 500m
Year 4 Autumn Term Kilometres Reasoning and Problem Solving James and Sita do a sponsored walk for charity. They walk 15km altogether. Complete the missing measurements so that each line of three gives a total distance of 2km. James walks double the amount that Sita walks. How far does Sita walk? They each raise 1 for every 500m they walk. How much money do they each make? James walks 10km Sita walks 5km James raises 20 James Sita Sita raises 10
Year 5 Autumn Term Teaching Guidance Convert Units of Length Notes and Guidance Children will use their knowledge of multiplying and dividing by 10, 100 and 1,000 to convert between different units of length. Teachers will support children to convert in both directions. E.g. from metres to kilometres and vice versa, where the number of decimal places given varies. 1 Varied Fluency Complete the statements below using =, < and > Mathematical Talk 2 Write the height of the 2 people in centimetres. How many millimetres are equivalent to one centimetre? How many centimetres are equivalent to one metre? How many metres are equivalent to one kilometre? What calculation do you need to do to convert between and? 3 What would their heights be in millimetres? A football pitch is 90 m long. A tennis court is 0.023 km long. How much longer is the football pitch in metres?
Year 5 Autumn Term Convert Units of Length Reasoning and Problem Solving A 5p coin has a thickness of 1.6 mm Sally makes a tower of 5p coins worth 90p A 1 coin has a thickness of 1.9 mm Emma makes a tower of 1 coins worth 8. Sally s tower: 18 x 1.6 mm = 28.8mm/2.88 cm Emma s tower: 8 x 1.9 mm = 15.2 mm/1.52 cm Difference: 2.88 cm 1.52 cm = 1.36 cm Molly, Daisy and Jess each need some ribbon for presents. The roll they have is 10 metres long. Molly needs 2.1 metres of ribbon. Daisy needs twice as much as Molly. Jess needs 15cm more than Molly. The girls think they will need more than 1 roll. Possible answer: I don t agree with them because they will need 210 cm + 420 cm + 225 cm which equals 855 cm. The roll holds 1000 cm so they will have enough. What is the difference in the height of the two towers in cm? Do you agree with them? Prove it.
Year 4 Autumn Term Teaching Guidance Perimeter on a Grid Notes and Guidance Children calculate the perimeter of rectilinear shapes by counting squares on a grid. They can use cm squares or work in pairs and groups on larger grids. They should be encouraged to explore which arrangements lead to longer perimeters and begin to see patterns linked to the way the squares are arranged. Mathematical Talk Can you estimate which of two shapes would have the longer perimeter? How do you decide where to start counting? Can you make a shape with double the perimeter? Can you make a shape with half the perimeter of shape x? When do you need to find the perimeter of a shape in real life? 1 2 3 Varied Fluency Work out the perimeter of the shape. Can you draw a different shape with : a) the same perimeter b) a perimeter which is 5cm longer c) a perimeter which is double/half the length of this one. Using squared paper draw two rectilinear shapes, each with a perimeter of 28cm What's the same and what's different about these shapes? Draw and find the perimeter of these shapes in cm.
Year 4 Autumn Term Perimeter on a Grid Reasoning and Problem Solving Which of these shapes has the longest perimeter? E has a greater perimeter it is 18 compared to 16 for T. Open ended Letters which could be drawn include: You have 10 paving stones to design a patio. The stones are one metre square. The stones must be joined to each other so that at least one edge is joined corner to corner. The shortest perimeter would be 14m in a 2x5 arrangement or 3x3 square with one added on. Explore other letters which could be drawn as rectilinear shapes. Put them in order of shortest to longest perimeter. B C D F I J L O P Letters with diagonal lines would be omitted. The longest would be 22m. Can you make a word? If heights of letters are kept the same, I or L could be the shortest. Use squared paper to show which design would give the longest perimeter and which would give the shortest.
Year 5 Autumn Term Teaching Guidance Measure Perimeter Notes and Guidance Children measure the perimeter of rectilinear shapes on a grid or by measuring with a ruler. It is important that children measure all the sides of the shape and label them as they work round the shape to ensure they measure accurately. 1 Varied Fluency Here is a shape drawn on a cm 2 grid. Draw the shape to scale and find the perimeter. Mathematical Talk 2 Use a ruler to measure the perimeter of the shape. What rules do I need to remember to ensure I am measuring accurately with a ruler? How can I make sure I don t miss any sides when measuring the perimeter? Can I use facts about opposite sides of a rectangle to check if I am accurate with my measuments? 3 Draw the following shapes to scale and find the perimeter of each shape. Order them from smallest to greatest A B C
Year 5 Autumn Term Measure Perimeter Reasoning and Problem Solving Each regular hexagon has sides measuring 2cm. Can you construct a shape with a perimeter of 44cm? Investigate the different ways you can make composite rectilinear shapes with a perimeter of 54cm. Possible answer
Year 4 Autumn Term Teaching Guidance Perimeter of a Rectangle Notes and Guidance In this step, children look at rectangles no longer on a square grid where some values may be missing. 1 Varied Fluency Work out the perimeter of the rectangles. They should explore different ways of expressing the calculation using known number facts including multiplication and division. 2cm 5cm 10cm Mathematical Talk What do you need to know to work out the perimeter? How do you know the value of each side? What shape is this? (square) If you only have the length of one side, how can you calculate the perimeter? What is a more efficient way of calculating the perimeter? 2 3 Work out the perimeter of the square. 8cm 4cm The perimeter of the rectangle is 36m. What is the length of the longest side? 6cm
Year 4 Autumn Term Perimeter of a Rectangle Reasoning and Problem Solving The width of a rectangle is 2 metres less than the length. The perimeter of the rectangle is between 20m and 30m. What could the dimensions of the rectangle be? Draw all the rectangles that fit these rules. Use 1cm=1m. The perimeter of a square is 16cm. How long is each side? If the perimeter 20m Length = 6m Width = 4m 24m Length = 7m Width = 5m 28m Length = 8m Width = 6cm 4cm Always, sometimes, never. When all the sides of a rectangle are odd numbers, the perimeter is even. Prove it. Here is a square. Each of the sides is whole number of metres. Which of these lengths could be the perimeter of the shape? 24m, 34m, 44m, 54m, 64m, 74m Always because when adding an odd and an odd they always equal an even number. 24cm Sides = 6cm 44cm Sides = 11cm 64cm Sides 16cm Why could the other values not be the perimeter?
Year 5 Autumn Term Teaching Guidance Calculate Perimeter Notes and Guidance Children calculate the perimeter of rectilinear shapes where they are given all the lengths. They use their addition skills to calculate the perimeter and use their number bonds to add more efficiently. Children draw a variety of shapes with the same perimeter. Mathematical Talk 1 2 Varied Fluency Here is a shape drawn on a centimetre squared grid. Label the length of each side of the shape. Calculate the perimeter of the shape. Calculate the perimeter of the rectilinear shapes. How can you ensure that you add up the length of every side? Do you have to add them in a specific order, can you look for number bonds to add more efficiently? Can you work systematically to draw a variety of shapes with the same perimeter? 15cm 4cm 14cm 7cm 10cm 8cm 9m 2.5m 6m 7.5m 3.5m 1.5m 3 How many hexagons can you draw with a perimeter of 30cm?
Year 5 Autumn Term Calculate Perimeter Reasoning and Problem Solving Here is a square inside another square. The perimeter of the inner square is 16cm The outer square s perimeter is four times the size of the inner square. What is the length of one side of the outer square? How do you Know? What do you notice? Small square = 16cm Large square = 64cm Length of one of the outer sides is 8cm, because 64 is a squared number. Here are two shapes. Shape A Shape B Stacey says The perimeter of shape B must be larger because it has more sides. Do you agree with Stacey? Explain your answer. Possible explanation: I do not agree with Stacey because the shapes have the same perimeter. Shape B has the same length and width overall as Shape A, the sides are just in a different direction to make it an irregular hexagon.
Year 4 Autumn Term Teaching Guidance Perimeter of Rectilinear Shapes Notes and Guidance In this step, children will begin to calculate perimeter of rectilinear shapes from diagrams without grids. They need to apply their knowledge of missing numbers to work out dimensions by finding the difference. Children need to have experience of drawing their own shapes in this step. Mathematical Talk Which measures are missing from the diagram? Explain to your partner why you think the line is cm long. Can you prove it? Can you make a rectilinear shape where your partner can work out the perimeter if you miss off the length of one of the sides? If you know the length of one side and part of the opposite side is known. Could you use a bar model to help? 1 2 3 Varied Fluency Find the perimeter of the shapes. The shape is made from 3 identical rectangles. Find the perimeter of the shape. How many different shapes can you make with a perimeter of 24cm? How many sides do they have?
Year 4 Autumn Term Perimeter of Rectilinear Shapes Reasoning and Problem Solving Here is a rectilinear shape. All the sides are the same length and are a whole number of centimetres. 48cm, 36cm or 120cm as there are 12 sides and these numbers are all multiples of 12 Bob has some rectangles all the same size. 3cm 8cm He makes this shape using his rectangles. What is the perimeter? Which of these lengths could be the perimeter of the shape? 48cm 36cm 80cm 120cm 66cm Any other answers suggested are correct if they are a multiple of 12 He makes another shape using the same rectangles. Calculate the perimeter of this shape. 54cm Can you think of any other answers which could be correct? 54cm
Year 5 Autumn Term Teaching Guidance Finding Unknown Lengths Notes and Guidance Varied Fluency Children apply their knowledge of measuring and finding perimeter to find unknown lengths. 1 Find the perimeter of the shapes. When calculating perimeter of shapes, encourage children to mark off the sides as they add them up to prevent repetition of counting/omission of sides. 3 cm 8 cm 10 cm 8.75 cm 12cm 19cm Mathematical Talk How can you use the sides you do know to calculate the missing lengths? Can you draw the shape to scale on centimetre squared paper to help you find the unknown lengths? 2 3 4 cm 16cm A square and a rectangle both have a perimeter of 24cm 2. Calculate the missing lengths. 4 cm How many rectangles can you draw where the length and width have a difference of 5 centimetres? What is the perimeter of each rectangle?
Year 5 Autumn Term Calculate Perimeter Reasoning and Problem Solving Harry calculates the perimeter of the shape as 20 centimetres. 3 cm 14 cm Is Harry correct? Explain your answer. 3 cm Harry is incorrect as he has only added up the sides that are labelled. The perimeter of the shape is 40 centimetres. The yellow rectangle has a perimeter of 38cm. What is the value of a? Total perimeter = 38cm 4.8 cm a 38 (4.8 + 4.8) = 28.4 So 28.4 divided by 2 = 14.2cm